A shared secret is a mechanism in cryptography which allows secure communication and data sharing between two or more entities. Secret sharing is a type of shared secret where the secret is broken into different parts (aka “secret shares”) and distributed among participants in a group of entities. The secret can be reconstructed only when a sufficient number of secret shares are obtained and combined together.
One known secret sharing scheme is Shamir secret sharing which involves generating a polynomial f(x) of a degree K−1, where the secret is the constant term a0 of the polynomial, and sharing points of the polynomial to N entities. A subset of K points retrieved from K entities is required for calculating the polynomial and obtaining the secret.
See the following reference which is incorporated herein by reference in its entirety: Adi Shamir “How to share a Secret”, Communications of the ACM, November 1979, 22 (11): 612-613, Blakley, G. R. (1979). “Safeguarding cryptographic keys”, Proceedings of the National Computer Conference 48: 313-317) For example, Adi Shamir in “How to share a Secret”, Communications of the ACM, November 1979, 22 (11): 612-613, Blakley, G. R. (1979). “Safeguarding cryptographic keys”, Proceedings of the National Computer Conference 48: 313-317. This